Invariant \((\alpha , \beta)\)-metrics on homogeneous manifolds
type: Item
instance of: scholarly article
title: Invariant \((\alpha , \beta)\)-metrics on homogeneous manifolds
zbMATH Open document ID: 1206.53022
author: Huihui An
author: Shaoqiang Deng
published in: Monatshefte für Mathematik
publication date: 2009-05-13T00:00:00Z
review text: The \((\alpha, \beta)\)-metrics in Finsler geometry have been introduced by \textit{M. Matsumoto} [Rep. Math. Phys. 31, No.~1, 43--83 (1992; Zbl 0772.53009)]. The authors construct invariant \((\alpha, \beta)\)-metrics on a homogeneous manifold from an invariant Riemannian metric and a vector field. Then, they find necessary and sufficient conditions for an \((\alpha, \beta)\)-metric to be of Berwald type or of Douglas type on a particular homogeneous space. Finally, they state necessary and sufficient conditions for invariant Kropina metrics and invariant Matsumoto metrics to be Berwald metrics on a homogeneous manifold.
reviewed by: Aurel Bejancu
Mathematics Subject Classification ID: 53B40
Mathematics Subject Classification ID: 53C30
zbMATH DE Number: 5553530
zbMATH Keywords: \((\alpha, \beta)\) metric
zbMATH Keywords: Berwald metric
zbMATH Keywords: Douglas metric
zbMATH Keywords: Randers metric
zbMATH Keywords: homogeneous spaces
MaRDI profile type: Publication
full work available at URL: s00605-007-0529-1
OpenAlex ID: W2065936603
cites work: Invariant Randers metrics on homogeneous Riemannian manifolds
cites work: The group of isometries of a Finsler space.
cites work: Invariant Finsler metrics on homogeneous manifolds
cites work: Theory of Finsler spaces with \((\alpha,\beta)\)-metric
cites work: Classes of Finsler spaces with \((\alpha,\beta)\)-metrics
DOI: 10.1007/S00605-007-0529-1
description: scientific article; zbMATH DE number 5553530